Dissolving cusp forms: Higher order Fermi's Golden Rules

For a hyperbolic surface embedded eigenvalues of the Laplace operator are unstable and tend to become resonances. A sufficient dissolving condition was identified by Phillips-Sarnak and is elegantly expressed in Fermi's Golden Rule. We prove formulas for higher approximations and obtain necessary and sufficient conditions for dissolving a cusp form with eigenfunction $u_j$ into a resonance. In the framework of perturbations in character varieties, we relate the result to the special values of the $L$-series $L(u_j\otimes F^n, s)$. This is the Rankin-Selberg convolution of $u_j$ with $F(z)^n$, where $F(z)$ is the antiderivative of a weight 2 cusp form. In an example we show that the above-mentioned conditions force the embedded eigenvalue to become a resonance in a punctured neighborhood of the deformation space.Comment: 33 pages, typos corrected, new section adde

Discrete logarithms in free groups

For the free group on n generators we prove that the discrete logarithm is distributed according to the standard Gaussian when the logarithm is renormalized appropriately.Comment: 9 pages, 1 figure, Corrects a mistake in the Introduction and Section

Serious Games in Cultural Heritage

Although the widespread use of gaming for leisure purposes has been well documented, the use of games to support cultural heritage purposes, such as historical teaching and learning, or for enhancing museum visits, has been less well considered. The state-of-the-art in serious game technology is identical to that of the state-of-the-art in entertainment games technology. As a result the field of serious heritage games concerns itself with recent advances in computer games, real-time computer graphics, virtual and augmented reality and artificial intelligence. On the other hand, the main strengths of serious gaming applications may be generalised as being in the areas of communication, visual expression of information, collaboration mechanisms, interactivity and entertainment. In this report, we will focus on the state-of-the-art with respect to the theories, methods and technologies used in serious heritage games. We provide an overview of existing literature of relevance to the domain, discuss the strengths and weaknesses of the described methods and point out unsolved problems and challenges. In addition, several case studies illustrating the application of methods and technologies used in cultural heritage are presented

Quantum Limits of Eisenstein Series and Scattering states

We identify the quantum limits of scattering states for the modular surface. This is obtained through the study of quantum measures of non-holomorphic Eisenstein series away from the critical line. We provide a range of stability for the quantum unique ergodicity theorem of Luo and Sarnak.Comment: 12 pages, Corrects a typo and its ramification from previous versio

The effect of Parylene coating on the surface roughness of PMMA after brushing

Acrylic resins, used in the manufacturing of different types of intra-oral prostheses, are vulnerable to, colonisation by microorganisms which potentially endanger the general health of the prostheses, wearers. The aim of this study was to investigate the influence of a novel coating (Parylene) on, surface roughness of poly-methyl-methacrylate (PMMA) samples after simulated cleansing using an, electric toothbrush and two brushing media (paste and pumice)

Predicting fraud in mobile money transfer using case-based reasoning

This paper proposes an improved CBR approach for the identification of money transfer fraud in Mobile Money Transfer (MMT) environments. Standard CBR capability is augmented by machine learning techniques to assign parameter weights in the sample dataset and automate k-value random selection in k-NN classification to improve CBR performance. The CBR system observes users’ transaction behaviour within the MMT service and tries to detect abnormal patterns in the transaction flows. To capture user behaviour effectively, the CBR system classifies the log information into five contexts and then combines them into a single dimension, instead of using the conventional approach where the transaction amount, time dimensions or features dimension are used individually. The applicability of the proposed augmented CBR system is evaluated using simulation data. From the results, both dimensions show good performance with the context of information weighted CBR system outperforming the individual features approach